Rupture Jumping Across Fault Stepovers: An Extension of Rupture-Tip Theory of Elongated Earthquakes

Stepovers between fault segments are a key structural control on rupture propagation, often determining whether ruptures terminate or cascade into large, multi-segment earthquakes. These dynamics critically influence earthquake magnitude and seismic hazard. Theoretical models, in particular the rupture-tip equation of motion for elongated ruptures (Weng & Ampuero, 2019), describe rupture growth along planar faults of finite widths. However, they do not account for the potential of rupture jumping across geometric discontinuities or frictional barriers. In this study, we use 2.5D dynamic rupture simulations with the spectral element method (SEM2DPACK software) to determine how the critical distance Hc for rupture jumping across stepovers in elongated fault systems of two parallel normal faults depends on prestress level S’ and seismogenic width W (Fig. a). We simulate dynamic rupture on a primary fault and record the resulting stress perturbations on a locked secondary fault. The critical stepover distance Hc​ is determined by computing the strength excess required for Coulomb failure on the secondary fault over a static process zone Lc. This approach is validated by complete dynamic rupture simulations in a selected set of fault stepover cases. For two co-planar faults we find a Hc/W ~ 1/S’ⁿ scaling relationship with n=2 for short Hc (near-field) and n=1/2 for large Hc (far-field) (Fig. b), consistent with dynamic nucleation thresholds with stepovers. For non-co-planar faults we find a Hc/W ~ 1/S’ⁿ scaling relationship with n=1 for near-field transitioning to n=2 for far-field (Fig. c). This transition is governed by the angular dependence of the stopping phase emitted by rupture arrest on the primary fault and the resulting dynamic trigger. These scaling relationships for co-planar and non-co-planar faults will be incorporated into the rupture-tip equation of motion, extending its applicability to segmented fault systems. The updated framework will improve assessment of rupture potential in complex fault networks, such as the 2023 Kahramanmaraş sequence (strike-slip), the 2010 Maule earthquake (subduction zone), and the 2016 Kaikōura earthquake (multifault rupture), as well as for induced earthquakes (e.g., the Groningen gas field). Particularly, extrapolating our results suggests that faults with small W need to be highly critically stressed to jump over even short distances (e.g., >94% stressed to jump over 300 m in Groningen’s 300 m wide gas reservoir). Since fault slip is expected to occur locally before reaching such high averaged stresses, this implies that rupture jumping in induced seismicity settings with small W is highly unlikely. These findings contribute to a unified theory of rupture propagation incorporating complex segmented systems.